Quantum mechanics can find a needle in a haystack every time

Abstract

Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The original formulation of Grover's algorithm is non-deterministic, finding the answer with a probability that varies with the size of the search space and the number of marked elements. A recent reformulation introduced a deterministic form of Grover's algorithm that - in principle - finds the answer with certainty. Here we realise the deterministic Grover's algorithm on a programmable photonic integrated circuit, finding that it not only outperforms the original Grover's algorithm as predicted, but is also markedly more robust against technological imperfections. We explore databases of 4 to 10 elements, with every choice of a single marked element, achieving an average success probability of $99.77 \pm 0.05\%$.